While yes, that's how a radiometer works (photons have so little momentum, their effects in normal power densities are minimal), they do carry momentum. They must - after all, they can transfer energy by losing energy themselves.
Further, here is the definition of energy, as from Albert Einstein:
E = (Pc)^2 + mc^2.
P, in this case, is the "relativistic" momentum, which is defined as:
P = p/sqrt(1-v^2/c^2). So if we can prove that P does not equal zero, then p (classical momentum) cannot be equal to zero.
Now, we know that photons have no "rest" mass. So let's set m = 0 in Einstein's equation.
E = (Pc)^2 + 0c^2
E = (Pc)^2
We know that photons carry energy, otherwise they wouldn't interact with anything.
So, the momentum of a photon must be
P = sqrt(E)/c, where E is the energy the photon carries. Now, it isn't much - E is relatively small and c is huge. However, it is something, i.e. P =/= 0. Therefore, "small" p cannot be equal to zero either.
Anyway, how could photons heat things up if they didn't "collide" with atoms and give them kinetic energy? After all, temperature is only the average kinetic energy of a large mass of molecules.